Question

Find θ if 0° < θ ≤ 90°.

`sin^2 θ + cos^2 30° = 5/4`

Answer 1

Given:

0° < θ ≤ 90°

`sin^2 θ + cos^2 30° = 5/4` 

cos 30° = `sqrt3/2 → cos^2 30° = 3/4`

`sin^2 θ = 5/4 − 3/4 = 1/2`

`sin θ = 1/sqrt2 = sqrt2/2`   [θ in first quadrant]

θ = 45°